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Inverse Power Pact (Posted on 2014-10-02) Difficulty: 3 of 5
Determine the value of a smallest positive integer N greater than 1 such that the base ten expansion of N1/N contains precisely six zeroes immediately following the decimal point. How about seven zeroes?

Extra Challenge: A non computer program solution.

No Solution Yet Submitted by K Sengupta    
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Solution The computer solution | Comment 1 of 2
DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents

 goalLT = 0.000001
 factor = 0.5
 n = 10000
 Do
   prevn = n
   p = n ^ (1 / n)
   frac = p - Int(p)
   prevdir = drct
   If frac >= goalLT Then
     drct = 1
     n = Int(n * (1 + factor) + 0.5)
   Else
     drct = -1
     n = Int(n * (1 - factor) + 0.5)
   End If
   If drct = -prevdir Then factor = factor / 2
   Text1.Text = Text1.Text & n & Str(p) & Str(factor) & crlf
   DoEvents
 Loop Until Abs(n - prevn) < 2
 
 
 Text1.Text = Text1.Text & crlf & " done"
End Sub

and a similar program with goalLT = 0.0000001 narrow down the search to allow manual exploration with the extra precision of UBASIC:

16626517^(1/16626517) = 1.0000010000000422...
16626518^(1/16626518) = 1.000000999999985677...


190660034^(1/190660034) = 1.0000001000000001398...
190660035^(1/190660035) = 1.0000000999999996428...

The two answers are bolded above.

  Posted by Charlie on 2014-10-02 10:47:53
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